{
 "cells": [
  {
   "cell_type": "markdown",
   "id": "73bd968b-d970-4a05-94ef-4e7abf990827",
   "metadata": {},
   "source": [
    "Chapter 17\n",
    "\n",
    "# 泰勒展开\n",
    "Book_3《数学要素》 | 鸢尾花书：从加减乘除到机器学习 (第二版)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ce1ca665-47bd-4cf1-856f-05423ced3f02",
   "metadata": {},
   "source": [
    "这段代码通过泰勒展开来研究函数\n",
    "\n",
    "$$\n",
    "f(x) = e^x\n",
    "$$\n",
    "\n",
    "在某个展开点 $x_0$ 处的逼近特性，并分析不同阶数的近似效果和误差。具体来说，代码在点 $x_0 = 0$ 处对 $f(x)$ 进行泰勒展开，并生成从 0 阶到 5 阶的多项式近似，通过可视化对比各阶数的泰勒展开与原函数的逼近情况。\n",
    "\n",
    "泰勒展开式表示为：\n",
    "\n",
    "$$\n",
    "f(x) \\approx f(x_0) + f'(x_0)(x - x_0) + \\frac{f''(x_0)}{2!}(x - x_0)^2 + \\cdots + \\frac{f^{(n)}(x_0)}{n!}(x - x_0)^n\n",
    "$$\n",
    "\n",
    "在 $f(x) = e^x$ 的情况下，由于 $f^{(n)}(x) = e^x$，在 $x_0 = 0$ 展开时各阶导数均为 1，因此展开式简化为：\n",
    "\n",
    "$$\n",
    "f(x) \\approx 1 + x + \\frac{x^2}{2!} + \\frac{x^3}{3!} + \\cdots + \\frac{x^n}{n!}\n",
    "$$\n",
    "\n",
    "代码通过绘制不同阶数的泰勒多项式（从 0 阶到 5 阶）来展示近似效果，并将这些近似曲线与原函数 $f(x)$ 进行对比，以观察随着阶数增加，近似如何逐渐逼近 $f(x)$。\n",
    "\n",
    "此外，代码还生成了误差分析图。以 2 阶泰勒展开为例，误差定义为：\n",
    "\n",
    "$$\n",
    "\\text{误差} = f(x) - f_{\\text{approx}}(x)\n",
    "$$\n",
    "\n",
    "其中 $f_{\\text{approx}}(x)$ 是二阶近似，即 $1 + x + \\frac{x^2}{2}$. 代码展示了误差在 $x$ 轴上的分布情况，表明在 $x_0$ 附近，误差较小，而远离 $x_0$ 时误差增大。这说明泰勒展开在展开点附近提供了良好的近似，但远离该点时近似精度降低。"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b505fb91-f240-4a21-8f79-92fb95021933",
   "metadata": {},
   "source": [
    "## 导入包"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "37c34312-a27d-43d1-b9f0-153e7e532d35",
   "metadata": {},
   "outputs": [],
   "source": [
    "from sympy import latex, lambdify, diff, sin, log, exp, series  # 导入符号计算库中用于导数、泰勒展开等功能\n",
    "from sympy.abc import x  # 定义符号变量 x\n",
    "import numpy as np\n",
    "from matplotlib import pyplot as plt  # 导入绘图库 Matplotlib\n",
    "from matplotlib import cm  # 导入颜色映射模块"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "62207524-16dc-4aac-9a56-e556281fc21c",
   "metadata": {},
   "source": [
    "## 定义待展开的函数 f(x) 并初始化 x 取值范围和展开点 x_0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "6dfa8693-5ef1-4e86-bf1c-1c1cfa1fa668",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/latex": [
       "$\\displaystyle e^{x}$"
      ],
      "text/plain": [
       "exp(x)"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "f_x = exp(x)  # 定义函数 f(x) = e^x\n",
    "f_x"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "d1448d76-9080-4b79-b0c4-cf6ee040fd24",
   "metadata": {},
   "outputs": [],
   "source": [
    "x_array = np.linspace(-2, 2, 100)  # 定义 x 的范围，用于绘制函数和展开项\n",
    "x_0 = 0  # 泰勒展开的中心点"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "64a8b06b-3ec6-402c-8b24-198d3b89b65a",
   "metadata": {},
   "outputs": [],
   "source": [
    "y_0 = f_x.evalf(subs={x: x_0})  # 计算 f(x_0) 的值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "c790ebfa-24f5-402b-9b07-c2c053b5e67d",
   "metadata": {},
   "outputs": [],
   "source": [
    "f_x_fcn = lambdify(x, f_x)  # 将符号函数转换为可数值化的函数\n",
    "f_x_array = f_x_fcn(x_array)  # 计算函数在 x_array 上的值"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "0a7ff2db-109d-4b25-99e7-08764a0e4abc",
   "metadata": {},
   "source": [
    "## 绘制函数和泰勒展开项"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "b279b09c-fb30-4f26-a152-c63f0cd35cf1",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x180b798da00>"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig, ax = plt.subplots()  # 创建绘图窗口\n",
    "\n",
    "ax.plot(x_array, f_x_array, 'k', linewidth=1.5)  # 绘制原函数 f(x)\n",
    "ax.plot(x_0, y_0, 'xr', markersize=12)  # 标记展开点 (x_0, y_0)\n",
    "ax.set_xlabel(r\"$\\it{x}$\")  # 设置 x 轴标签\n",
    "ax.set_ylabel(r\"$\\it{f}(\\it{x})$\")  # 设置 y 轴标签\n",
    "\n",
    "highest_order = 5  # 设置泰勒展开的最高阶数\n",
    "order_array = np.arange(0, highest_order + 1)  # 定义阶数数组\n",
    "colors = plt.cm.rainbow(np.linspace(0, 1, len(order_array)))  # 使用彩虹色映射不同阶数\n",
    "\n",
    "i = 0  # 颜色索引初始化\n",
    "\n",
    "## 绘制不同阶的泰勒展开近似\n",
    "for order in order_array:\n",
    "    f_series = f_x.series(x, x_0, order + 1).removeO()  # 计算泰勒展开项（去除高阶小量）\n",
    "    f_series_fcn = lambdify(x, f_series)  # 将展开项转换为数值函数\n",
    "    f_series_array = f_series_fcn(x_array)  # 计算展开项在 x_array 上的值\n",
    "\n",
    "    ax.plot(x_array, x_array * 0 + f_series_array, linewidth=0.5, color=colors[i, :], label='Order = %0.0f' % order)  # 绘制展开项\n",
    "    i += 1  # 更新颜色索引\n",
    "\n",
    "ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格\n",
    "ax.set_xlim(x_array.min(), x_array.max())  # 设置 x 轴范围\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右侧边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏顶部边框\n",
    "\n",
    "plt.legend()  # 添加图例"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5922ac18-78b9-4bd7-85e2-d023cb0507ce",
   "metadata": {},
   "source": [
    "## 误差分析图"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "36ac1d7e-84de-49d0-80c3-ec2fc80bda58",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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",
      "text/plain": [
       "<Figure size 960x480 with 2 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=plt.figaspect(0.5))  # 创建一个具有宽比例的图形\n",
    "ax = fig.add_subplot(1, 2, 1)  # 左图绘制原函数和展开项\n",
    "\n",
    "ax.plot(x_array, f_x_array, 'k', linewidth=1.5)  # 绘制原函数 f(x)\n",
    "ax.plot(x_0, y_0, 'xr', markersize=12)  # 标记展开点 (x_0, y_0)\n",
    "ax.set_xlabel(r\"$\\it{x}$\")  # 设置 x 轴标签\n",
    "ax.set_ylabel(r\"$\\it{f}(\\it{x})$\")  # 设置 y 轴标签\n",
    "\n",
    "highest_order = 2  # 设置误差分析的展开阶数\n",
    "\n",
    "f_series = f_x.series(x, x_0, highest_order + 1).removeO()  # 计算最高阶数为 2 的泰勒展开\n",
    "f_series_fcn = lambdify(x, f_series)  # 转换为数值函数\n",
    "f_series_array = f_series_fcn(x_array)  # 计算展开项在 x_array 上的值\n",
    "f_series_array = x_array * 0 + f_series_array  # 保持数组形状一致\n",
    "\n",
    "ax.plot(x_array, f_series_array, linewidth=1.5, color='b')  # 绘制二阶展开的近似曲线\n",
    "\n",
    "ax.fill_between(x_array, f_x_array, x_array * 0 + f_series_array, color='#DEEAF6')  # 用颜色填充误差区域\n",
    "\n",
    "ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格\n",
    "ax.set_xlim(x_array.min(), x_array.max())  # 设置 x 轴范围\n",
    "ax.set_ylim(np.floor(f_x_array.min()), np.ceil(f_x_array.max()))  # 设置 y 轴范围\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右侧边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏顶部边框\n",
    "\n",
    "ax = fig.add_subplot(1, 2, 2)  # 右图绘制误差\n",
    "\n",
    "error = f_x_array - f_series_array  # 计算误差\n",
    "ax.plot(x_array, error, 'r', linewidth=1.5)  # 绘制误差曲线\n",
    "ax.fill_between(x_array, error, color='#DEEAF6')  # 用颜色填充误差区域\n",
    "plt.axhline(y=0, color='k', linestyle='--', linewidth=0.25)  # 添加 y=0 的参考线\n",
    "ax.set_xlabel(r\"$\\it{x}$\")  # 设置 x 轴标签\n",
    "ax.set_ylabel(\"Error\")  # 设置 y 轴标签\n",
    "\n",
    "ax.grid(linestyle='--', linewidth=0.25, color=[0.5, 0.5, 0.5])  # 添加网格\n",
    "ax.set_xlim(x_array.min(), x_array.max())  # 设置 x 轴范围\n",
    "ax.set_ylim(np.floor(error.min()), np.ceil(error.max()))  # 设置 y 轴范围\n",
    "ax.spines['right'].set_visible(False)  # 隐藏右侧边框\n",
    "ax.spines['top'].set_visible(False)  # 隐藏顶部边框"
   ]
  }
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